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Nonasymptotic performance analysis of importance sampling schemes for small noise diffusions

Part of: Limit theorems Stochastic processes

Published online by Cambridge University Press:  30 March 2016

Konstantinos Spiliopoulos
Konstantinos Spiliopoulos*
Affiliation:
Boston University
*
∗ Postal address: Department of Mathematics and Statistics, Boston University, Boston, MA 02215, USA. Email address: kspiliop@math.bu.edu
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Abstract

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In this paper we develop a prelimit analysis of performance measures for importance sampling schemes related to small noise diffusion processes. In importance sampling the performance of any change of measure is characterized by its second moment. For a given change of measure, we characterize the second moment of the corresponding estimator as the solution to a partial differential equation, which we analyze via a full asymptotic expansion with respect to the size of the noise and obtain a precise statement on its accuracy. The main correction term to the decay rate of the second moment solves a transport equation that can be solved explicitly. The asymptotic expansion that we obtain identifies the source of possible poor performance of nevertheless asymptotically optimal importance sampling schemes and allows for a more accurate comparison among competing importance sampling schemes.

Keywords

Importance samplingMonte Carlolarge deviationasymptotic expansion

MSC classification

Primary: 60F05: Central limit and other weak theorems
Secondary: 60F10: Large deviations 60G60: Random fields
Type
Research Papers
Information
Journal of Applied Probability , Volume 52 , Issue 3 , September 2015 , pp. 797 - 810
Copyright
Copyright © 2015 by the Applied Probability Trust 

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